Solve for $b$. Give an exact answer. $0.75(8b+4)-1=4b+14$ $b =$
Answer: We need to manipulate the equation to get $ b $ by itself. $\begin{aligned} 0.75(8b+4)-1 &= 4b+14 \\\\ 6b+3-1 &= 4b+14~~~~~~~~~~\gray{\text{Distribute}}\\\\ 6b+2 &= 4b+14~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 6b+2{-4b} &= 4b+14{-4b} ~~~~~~~~~~\gray{\text{Subtract 4b from each side}}\\\\ 2b+2 &=14 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 2b+2{-2} &=14 {-2} ~~~~~~~~~~\gray{\text{Subtract 2 from each side}}\\\\ 2b &=12 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{2b}{{2}}&= \dfrac{12}{{2}}~~~~~~~~~~\gray{\text{Divide each side by 2}} \\\\ b &= {6} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $ b= { 6 }~~~~~~~~$ [Let's check our work!]